Electrical Engineering homework help. ELEG-548: Low Power VLSI Circuit Design, Spring 2020, Homework #2.

1. (15’) A CMOS inverter is shown in Figure 1. Assume for every clock cycle Tclk=100ns, one test

pattern is applied at input. For time period t=0~3600ns, the input waveform (Vin) is shown in the

figure. Vdd=5V, threshold voltage of NMOS/PMOS transistor: Vtn=-Vtp=0.8V, load capacitance

CL=24pF.

1). Sketch the output waveform (Vout) for given input pattern (Vin) during t=0~3600ns. Based on

the waveform, find the average switching activity Asw , 0→1 switching probability α0→1, and 1→0

switching probability α1→0 of output signal Vout during time period t=0~3600ns.

2). If only transition power is considered, during time period t=0~3600ns, how much energy is

drawn from voltage source Vdd? How much total thermal energy (heat) is generated?

3). Find the average transition power Ptran_avg of output node (out) during time period t=0~3600ns.

4). Given input rising/falling time: tr=tf=0.2ns, maximum short circuit current at input rising/falling

transition: Iscmaxr=Iscmaxf=0.4µA. Calculate the average short circuit power Psc_avg of the CMOS

inverter during time period t=0~3600ns.

5). If load capacitance CL is decreased from 24pF to 6pF, will the average transition power Ptran_avg

at output node be increased or decreased? Why? Will the average short-circuit power Psc_avg of the

CMOS inverter be increased or decreased? Why? Please use 2~3 sentences to briefly explain the

reason for each case.

Figure 1. CMOS inverter

2. (15’) For short circuit power Psc of an inverter in Figure 2, if input Vin has a 1→0 switching,

Figure 2. Inverter with load capacitance CL

1). If the size (W/L ratio) of the transistors increases, will the short circuit power be increased or

decreased? Why? Does this change the time period (tE-tB) or the peak value of short-circuit current,

or both? If we want to reduce the lasting period (tE-tB) of the short-circuit current, what should we

do?

2). If input Vin has a 1→0 switching, which transistor current (Idsp of PMOS or Idsn of NMOS) will

be the bottleneck to decide the overall short-circuit current? If the load capacitance CL increases,

will the short circuit current be increased or decreased? Why? Please draw a figure to explain it.

3). Assume 50 consecutive input patterns are applied to the inverter, and each pattern lasts for 20ns.

During this time period T=1000ns, the inverter input makes 26 rising transitions and 26 falling

transitions. Given Vdd=5V, Vtp=-0.7V, Vtn=0.8V, input rising time tr=0.1ns, input falling time

tf=0.2ns, maximum short-circuit current for input rising transition is Iscmaxr=120nA, maximum short-

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circuit current for input falling transition is Iscmaxf=160nA. What is the total short-circuit energy Esc

consumed during this time period? What is the average short circuit power Psc_avg during this time

period T=1000ns?

3.(15’) Consider a VLSI chip with 430 million transistors. It consists of both static CMOS logic

gates and memory. Among them, there are 280 million logic gate transistors with average transistor

width of 12λ/transistor, and 150 million memory transistors with average transistor width of

4λ/transistor. Assume that clock signal is routed on a metal layer with average width of 1.6µm and

overall length of 160mm. The parasitic capacitance of metal layer for clock wire is 1.8fF/µm2

.

Assume Vdd=5V, feature size of fabrication process is 2λ=64nm, gate capacitance per transistor

width Cg=2fF/mm. For static CMOS logic gates, average switching activity Asw=0.6, for memory

arrays, the average switching activity Asw=0.4; for clock wire, average switching activity Asw=2.

The VLSI chip works at frequency f=3.2GHz. Neglect other wire capacitance except for the clock

wire. What is the average transition power Ptran of the VLSI chip? (Hint: Total transition power =

logic transition power + memory transition power + clock wire transition power)

4.(15’) A CMOS 2-input AND gate is shown in Figure 3. If we wish to use PSPICE power

simulation to simulate its average power consumption for time period T=400ns. During this time

period, 4 input patterns were input to the AND gate, with each pattern lasting for 100ns. Assume

Vdd=5V.

1). Draw the schematic for the PSPICE power simulation circuit. You need to clearly draw the

AND gate and the auxiliary power measurement circuitry in transistor level, and the connection

between them. Please do NOT use a block diagram to represent the original circuit.

2). Assume in power measurement circuitry, R=900kΩ, C=220pF, what value should the controlling

coefficient (K) of the current controlled current source be set to?

3). After PSPICE power simulation, the voltage waveform across the capacitance C is shown in

Figure 4. From Figure 4, what is the average power consumption Pavg and total energy consumption

E of the AND gate during time period T=400ns? What is the average power consumption Pavg and

total energy consumption E of the AND gate during time period t=0~280ns? Shade the area in

Figure 4 which represents the energy consumption of the AND gate during time period t=0~280ns.

Figure 3. A CMOS 2-input AND gate

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Figure 4. PSPICE power simulation curve

5.(20’) Consider a CMOS logic circuit (implemented using static CMOS technology) driving a XY

pF load capacitance as shown in Figure 5, where “XY” are the last two digits of your student ID.

For example, if the last 2 digits of your student ID are “56”, then it’s 56pF. Also, the characteristics

of the cell library are shown below. Input capacitance of a gate is the parasitic capacitance between

each input and ground; output capacitance of a gate is the parasitic capacitance between each output

and ground. Assume the probabilities for the inputs to be “1” (“1” probability) are:

p(A)=p(B)=0.2, p(C)=p(D)= 0.6

1). Find the “1” probabilities for nodes E, F, G.

2). Calculate switching capacitances for nodes A, B, C, D, E, F, G.

3). Assume Vdd=5V, clock frequency (the frequency of applied patterns) fclk=300MHz. Calculate

average switching power for the whole circuit. (Hint: total switching power of a circuit is the sum

of the switching power of all the nodes.)

Table 1. Characteristics of 0.8μm CMOS cell library

Gate type Area Output Capacitance(fF) Input Capacitance (fF) Average delay (ns)

INV 2 80 48 0.22+1.00C0

NOR3 4 102 48 0.37+1.5C0

NAND2 3 136 48 0.27+1.5C0

Figure 5. A CMOS logic circuit

6.(20’) A CMOS circuit is shown in Figure 6. Assume “1”-probabilities of two inputs are: p(A)=0.5,

p(B)=0.5.

1). Derive the logic function of the gate output (F) (Note: You need to simplify your logic

expression for F). What is the function of this CMOS circuit?

2). Is there any signal correlation between nodes C and D? If yes, clearly explain the correlation.

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3). Based on Question 2), Calculate the “1”-probabilities of nodes C, D, and F. Clearly show your

calculation procedures for each node.

4). Based on the results, use equation to calculate the switching probability (Psw) of F.

5). List the switching table for output F. Based on the switching table, derive the switching

probability of output F. Is it in good agreement with your result obtained in Question 4)?

Figure 6. A CMOS circuit

Due: 02/27/2020 (Thursday) in class